Britain yesterday warned of an "epic" humanitarian disaster unfolding in Burma in the wake of the cyclone, even as international relief finally began to trickle into the stricken country.

The foreign secretary, David Miliband, criticised the military regime over its failure to swiftly open up to international aid for its suffering millions and predicted that if it did not alter course soon the massive death toll could rise dramatically.

The blunt message over the generals' lack of urgency came as aid agencies echoed his fear, warning of an "unimaginable tragedy" if significant amounts of relief did not arrive quickly to stave off disease. The mounting alarm surfaced even as more flights loaded with emergency supplies landed in Rangoon yesterday. They were quickly offloaded and the aid destined for the needy in the hardest-hit Irrawaddy delta region south-west of the main city, Rangoon.

But one aid agency said it represented a "drop in the ocean" compared with the scale of the catastrophe brought about by Cyclone Nargis eight days ago. The official death toll reached 28,453, while the number of missing fell to 33,416, though the UN believes 100,000 died.

"I would be amazed if there haven't been 100,000 people dead already," Miliband told the BBC. "What's more, hundreds of thousands more are at risk and a natural disaster is turning into a humanitarian crisis of genuinely epic proportions, in significant part because of what I would call the malign neglect of the regime."

The international development secretary, Douglas Alexander, said he was "horrified" by the wrangling of the past week as the Burma leadership was condemned for its callous response to the tragedy, barring access to most international disaster relief specialists and blocking aid.

But Alexander noted a slight improvement after a British disaster assessment team had got into the country, matched by the increasing pace of the number of aid flights landing in Burma at the weekend.

Yesterday, Save the Children said it had monitored the unloading of a UN refugee agency flight carrying 32 tonnes of tents and plastic sheeting at Rangoon and the contents were quickly taken to the Irrawaddy delta to the homeless, estimated at up to 1.9 million people.

The UN's World Food Programme also got clearance for the 38 tonnes of high-energy biscuits that had been impounded on Friday by the Burmese authorities. With another 17 tonnes airlifted and taken to bases in the delta, it was enough to feed 27,400 people. The Red Cross said it had also managed to get a fourth flight into Rangoon with others due today, bringing in tonnes of medical supplies.

However, its relief efforts suffered a setback that underlined the difficulty of the environment when a boat it had chartered hit submerged logs while on the 12-hour journey from Rangoon to Bogalay. The crew steered it to an island and scrambled off, but it sank taking rice, water and other aid for 1,000 people with it.

Aid agencies reported that the cyclone's survivors were increasingly moving out of the delta - in some cases relocated by the Burmese authorities - to camps on the fringes of the worst affected areas.

The UN said that about 206,000 people were crowded into 218 camps, often schools, monasteries or temples that withstood the cyclone's force and the tidal wave that washed over the delta. In Laputta, one of the most devastated towns where 95% of the buildings were damaged or destroyed, as many as 150,000 people were crammed into the shelters.

Jonathan Pearce, of the British medical charity Merlin, already working in Laputta before the tragedy, said that 50 of its volunteers out of 600 were unaccounted for and were presumed to be dead. "One of our international staff who came back from Laputta - a seasoned guy who has worked many disasters - could not recall anything like what he saw there," said Pearce. "When you see aid workers like that crying it's very unusual."

But agencies are concerned that without proper sanitation and clean water people still scavenging in the inundated remains of their homes could fall victim to waterborne diseases. "Everything hinges on access," said Greg Beck, of the International Rescue Committee. "Unless there is fast infusion of aid, there is going to be a tragedy of an unimaginable scale."

Oxfam warned that in the coming weeks and months 1.5 million survivors could be in danger. "With the likelihood of 100,000 or more killed in the cyclone there are all the factors for a public health catastrophe which could multiply that death toll by up to 15 times," said Sarah Ireland, Oxfam's east Asia director.

Samson Jeyakumar, director of the children's programme for World Vision which has 580 staff in Burma, warned: "There are reports of diarrhoea now. Cholera is a matter of time, and it can happen any time."